Evolution is the unifying theme of biology, and consequently a vital force in medicine. In general terms, mutants that arise in populations may spread through selection or random drift, changing the nature of the population over time. Two of the most prominent features of any population-be it people, pathogens, or cells in the human body-are its size and structure. Yet how size and structure affect the evolution of a population remains poorly understood. Evolutionary graph theory is a promising new approach for investigating these issues. The population of interest is represented as a graph, whereby individuals are represented as nodes and relationships between individuals are represented as arcs or edges. The number of nodes reflects the size of the population, while the topology of the graph represents its structure. Preliminary work has focused on fixation probabilities of mutants in populations of various sizes and structures. Among the most exiting findings was that structure can completely alter the trajectory of evolution by amplifying the power of selection or drift relative to unstructured populations. This finding raises the intriguing possibility that structures in the body, such as ducts in glandular tissues and germinal centers in lymph nodes, suppress or amplify selection in ways that influence, for example, the emergence of cancer or the ability to mount successful immune responses. This proposal has three general goals: (i) to move the theory forward from a static description of fixation probabilities and unchanging structures to a dynamic understanding of fixation rates and evolving structures;(ii) to apply this work to understand how structure-for example, lineage relationships in the hematopoietic system and tissue microarchitecture in crypts, villi, ductules, acini, and the lymphoid organs-affects the somatic evolution of cancer;and (iii) to design experiments for testing evolutionary graph theory using microfluidic technology and resources available from pathology. The results promise a new structuralevolutionary framework for understanding processes that are of vital importance to medicine.